Gravitational form factors of light nuclei: Impulse approximation

The gravitational form factors of light nuclei are evaluated up to momenta of the order of the nucleon mass, using the impulse approximation. The nucleon gravitational form factors are reduced nonrelativistically, and used to derive the gravitational form factors of light nuclei. The deuteron gravitational form factors are analysed using the Reid soft core potential. The helium-4 gravitational form factors are assessed using the $K$-harmonics method, and compared to those following from a mean-field approximation with a Woods-Saxon potential. The importance of removing the center of mass motion for the ensuing form factors is emphasized. The mass radii of these light nuclei are extracted and compared to their charge radii counterparts. The details of their pressure and shear distributions are discussed.

Figure 1

Top: Reid soft core potentials $V_{C,T,LS}$; bottom: deutron $S,D$ wave functions in Eq. (4).

Figure 2

Nucleon GFFs: $A_q,C_q$ (quarks) are from the recent lattice results [21], and $A_g,C_g$ (gluons) are from the holographic model [22].

Figure 3

A graviton through $T^{\mu \nu }\left(k\right)$, striking a nucleon in a deuteron with a recoiling spectator of momentum $-P$.

Figure 4

The deuteron invariant EMT form factors (38) in the impulse approximation: gluon (red-dashed line), quark (blue-dotted line), and $\text{gluon}+\text{quark}$ (black-solid line), compared to the nucleon $A^N$ and $D^N$ (thinner dashed, dotted, and solid lines).

Figure 5

The gluon and quark pressure $p_{0,2,3}$ and shear $s_{0,2,3}$ distributions inside the deuteron, in the impulse approximation.

Figure 6

Top: The potential $W\left(R\right)$ and $V_C\left(R\right)$ defined in Eqs. (60) and (62). $W_1, W_2$, and $W_3$ are obtained using $V_1, V_2$, and $V_3$ defined in Eqs. (63) and (64). Bottom: Helium-4 $S$ wave reduced wave function solution with potential $V_1, V_2$, and $V_3$ versus the hyperdistance.

Figure 7

Top: Woods-Saxon potentials $V_{WS}$ for helium-4. Bottom: Helium-4 $S$ wave.

Figure 8

$A$- and $D$-form factors for helium-4 obtained using $K$-harmonics method with potential $V_3$.

Figure 9

$A$- and $D$-form factors for helium-4 obtained using a Woods-Saxon potential.

Figure 10

The gluon and quark pressure $p_{g,q}$ and shear $s_{g,q}$ distributions in helium-4 using $K$-harmonics method (top) and Woods-Saxon potential (bottom), in the impulse approximation.

Figure 11

The spin average $D$ form factor normalized by the baryon number $A$ in the nucleon ($N$), deuteron ($D$), and helium-4 ($\mathrm{HE}$) with sublabels for $K$ harmonics with potentials $V_3$ and Woods-Saxon.

Figure 12

Top: Deuteron electric charge form factors in the impulse approximation compared to experiment [46]. Bottom: Helium-4 electric charge form factors using the $K$-harmonics method with the potentials in Eqs. (63) and (64) and the Woods-Saxon potential, compared to experiment [47].